U3Gate

class qiskit.circuit.library.U3Gate(theta, phi, lam, label=None)

Bases: Gate

Generic single-qubit rotation gate with 3 Euler angles.

Warning

This gate is deprecated. Instead, the following replacements should be used

U3(\theta, \phi, \lambda) = U(\theta, \phi, \lambda)

circuit = QuantumCircuit(1)
circuit.u(theta, phi, lambda)

Circuit symbol:

     ┌───────────┐
q_0: ┤ U3(ϴ,φ,λ) ├
     └───────────┘

Matrix Representation:

\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}U3(\theta, \phi, \lambda) = \begin{pmatrix} \cos\left(\th\right) & -e^{i\lambda}\sin\left(\th\right) \\ e^{i\phi}\sin\left(\th\right) & e^{i(\phi+\lambda)}\cos\left(\th\right) \end{pmatrix}\end{split}

Note

e^{i(\phi+\lambda)/2}

Examples:

U3(\theta, \phi, \lambda) = e^{-i \frac{\pi + \theta}{2}} P(\phi + \pi) \sqrt{X} P(\theta + \pi) \sqrt{X} P(\lambda)

U3\left(\theta, -\frac{\pi}{2}, \frac{\pi}{2}\right) = RX(\theta)

U3(\theta, 0, 0) = RY(\theta)

Create new U3 gate.

Attributes

Get Clbits in condition.

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

Return definition in terms of other basic gates.

Get the duration.

Return instruction label

Return the name.

Return the number of clbits.

Return the number of qubits.

return instruction params.

Get the time unit of duration.

control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a (multi-)controlled-U3 gate.

Parameters

num_ctrl_qubits (int) – number of control qubits.
label (str or None) – An optional label for the gate [Default: None]
ctrl_state (int orstr or None) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.

Returns

controlled version of this gate.

Return type

ControlledGate

inverse()

Return inverted U3 gate.

U3(\theta,\phi,\lambda)^{\dagger} =U3(-\theta,-\lambda,-\phi)

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